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{{Short description|Change in velocity per amount of fuel}}
'''Specific impulse''' (usually abbreviated ''I''<sub>sp</sub>) is a way to describe the ] and ] engines' efficiency. It represents the ] with respect to the amount of ] used per unit time.<ref name="QRG1">{{cite web|url=http://www.qrg.northwestern.edu/projects/vss/docs/propulsion/3-what-is-specific-impulse.html|title=What is specific impulse?|publisher=Qualitative Reasoning Group|accessdate=22 December 2009}}</ref> If the "amount" of propellant is given in terms of ] (such as in kilograms), then specific impulse has units of ]. If it is given in terms of weight (like ]s or ]), then specific impulse has units of time (seconds). The conversion constant between the two versions of specific impulse is ''']'''.<ref name="SINasa">{{cite web|url=http://www.grc.nasa.gov/WWW/K-12/airplane/specimp.html|title=Specific impulse|last=Benson|first=Tom|date=11 July 2008|publisher=NASA|accessdate=22 December 2009}}</ref> The higher the specific impulse, the lower the propellant ] required for a given ], and in a rocket the less propellant needed for a given ] per the ].
{{Use dmy dates|date=March 2020}}


'''Specific impulse''' (usually abbreviated {{math|''I''<sub>sp</sub>}}) is a measure of how efficiently a ] engine, such as a ] using propellant or a ] using fuel, generates ]. In general, this is a ratio of the '']'', i.e. change in momentum, ''per mass'' of propellant. This is equivalent to "thrust per massflow". The resulting unit is equivalent to velocity, although it doesn't represent any physical velocity (see below); it is more properly thought of in terms of momentum per mass, since this represents a physical momentum and physical mass.
The '''actual exhaust velocity''' is the average speed of the exhaust jet as it leaves the vehicle. The '''effective exhaust velocity''' is the exhaust velocity that would be required to produce the same thrust in a vacuum. The two are identical for an ideal rocket working in a vacuum, but are radically different for an ] that obtains extra thrust by accelerating air. Specific impulse and effective exhaust velocity are proportional.


The practical meaning of the measurement varies with different types of engines. Car engines consume onboard fuel, breathe environmental air to burn the fuel, and react (through the tires) against the ground beneath them. In this case, the only sensible interpretation is momentum per fuel burned. Chemical rocket engines, by contrast, carry aboard all of their combustion ingredients and reaction mass, so the only practical measure is momentum per reaction mass. Airplane engines are in the middle, as they only react against airflow through the engine, but some of this reaction mass (and combustion ingredients) is breathed rather than carried aboard. As such, "specific impulse" could be taken to mean either "per reaction mass", as with a rocket, or "per fuel burned" as with cars. The latter is the traditional and common choice. In sum, specific impulse isn't practically comparable between different types of engines.
Specific impulse is a useful value to compare engines, much like ''miles per gallon'' or ''liters per 100 kilometers'' is used for cars.<ref name=sutton/> A propulsion method with a higher specific impulse is more propellant-efficient.<ref name="QRG1" /><ref name=ars20130414>
{{cite news|last=Hutchinson|first=Lee |title=New F-1B rocket engine upgrades Apollo-era design with 1.8M lbs of thrust |url=http://arstechnica.com/science/2013/04/new-f-1b-rocket-engine-upgrades-apollo-era-deisgn-with-1-8m-lbs-of-thrust/ |accessdate=15 April 2013 |newspaper=ARS technica |date=14 April 2013 |quote=''The measure of a rocket's fuel efficiency is called its specific impulse (abbreviated as "ISP"—or more properly Isp). ... 'Mass specific impulse...describes the thrust-producing efficiency of a chemical reaction and it is most easily thought of as the amount of thrust force produced by each pound (mass) of fuel and oxidizer propellant burned in a unit of time. It is kind of like a measure of miles per gallon (mpg) for rockets.<nowiki>'</nowiki>''}}</ref>
Another number that measures the same thing, usually used for air breathing jet engines, is ]. Specific fuel consumption is inversely proportional to specific impulse and effective exhaust velocity.


In any case, specific impulse can be taken as a measure of efficiency. In cars and planes, it typically corresponds with fuel mileage; in rocketry, it corresponds to the achievable ]<ref name="QRG1">{{cite web|url=http://www.qrg.northwestern.edu/projects/vss/docs/propulsion/3-what-is-specific-impulse.html|title=What is specific impulse?|publisher=Qualitative Reasoning Group|access-date=22 December 2009|archive-date=4 July 2016|archive-url=https://web.archive.org/web/20160704233223/http://www.qrg.northwestern.edu/projects/vss/docs/Propulsion/3-what-is-specific-impulse.html|url-status=dead}}</ref><ref name="ars20130414">{{cite web|last=Hutchinson|first=Lee |title=New F-1B rocket engine upgrades Apollo-era design with 1.8M lbs of thrust |url=https://arstechnica.com/science/2013/04/new-f-1b-rocket-engine-upgrades-apollo-era-deisgn-with-1-8m-lbs-of-thrust/ |access-date=15 April 2013 |website=] |date=14 April 2013 |quote=The measure of a rocket's fuel effectiveness is called its specific impulse (abbreviated as 'ISP'—or more properly Isp).... 'Mass specific impulse ... describes the thrust-producing effectiveness of a chemical reaction and it is most easily thought of as the amount of thrust force produced by each pound (mass) of fuel and oxidizer propellant burned in a unit of time. It is kind of like a measure of miles per gallon (mpg) for rockets.'}}</ref>, which is the typical way to measure changes between orbits.
==General considerations==
The amount of propellant is normally measured either in units of mass or weight. If mass is used, specific impulse is an impulse per unit mass, which ] shows to be a unit of speed, and so specific impulses are often measured in meters per second and are often termed '''effective exhaust velocity'''. However, if propellant weight is used instead, an impulse divided by a force (weight) turns out to be a unit of time, and so specific impulses are measured in seconds. These two formulations are both widely used and differ from each other by a factor of '']'', the dimensioned ] of ] at the surface of the Earth.


] traditionally uses a "bizarre" choice of units: rather than speaking of momentum-per-mass, or velocity, the rocket industry typically converts units of velocity to units of time by dividing by a standard reference acceleration, that being ] g{{sub|0}}. This is a historical result of competing units, ] vs ]. They shared a common unit of time (seconds) but not common units of distance or mass, so this conversion by reference to g{{sub|0}} became a standard way to make international comparisons. This choice of reference conversion is arbitrary and the resulting units of time have no physical meaning. The only physical quantities are the momentum change and the mass used to achieve it.
Note that the rate of gain of momentum of a rocket (including fuel) per unit time is equal to the thrust.


==Propulsion systems==
The higher the specific impulse, the less propellant is needed to produce a given thrust during a given time. In this regard a propellant is more efficient if the specific impulse is higher. This should not be confused with energy efficiency, which can even decrease as specific impulse increases, since propulsion systems that give high specific impulse require high energy to do so.<ref>http://www.geoffreylandis.com/laser_ion_pres.htp</ref>


===Rockets===
In addition it is important that ] and specific impulse not be confused with one another. The specific impulse is a measure of the ''impulse per unit of propellant'' that is expended, while thrust is a measure of the momentary or peak force supplied by a particular engine. In many cases, propulsion systems with very high specific impulses—some ]s reach 10,000 seconds—produce low thrusts.<ref name="exploreMarsnow">{{cite web|url=http://www.exploremarsnow.org/MissionOverview.html|title=Mission Overview|publisher=exploreMarsnow|accessdate=23 December 2009}}</ref>
For any chemical rocket engine, the momentum transfer efficiency depends heavily on the effectiveness of the ]; the nozzle is the primary means of converting reactant energy (e.g. thermal or pressure energy) into a flow of momentum all directed the same way. Therefore, nozzle shape and effectiveness has a great impact on total momentum transfer from the reaction mass to the rocket.


Efficiency of conversion of input energy to reactant energy also matters; be that thermal energy in combustion engines or electrical energy in ], the engineering involved in converting such energy to outbound momentum can have high impact on specific impulse. Specific impulse in turn has deep impacts on the achievable delta-v and associated orbits achievable, and (by the rocket equation) mass fraction required to achieve a given delta-v. Optimizing the tradeoffs between mass fraction and specific impulse is one of the fundamental engineering challenges in rocketry.
When calculating specific impulse, only propellant that is carried with the vehicle before use is counted. For a chemical rocket the propellant mass therefore would include both fuel and ]; for air-breathing engines only the mass of the fuel is counted, not the mass of air passing through the engine.


Although the specific impulse has units equivalent to velocity, it almost never corresponds to any physical velocity. In chemical and cold gas rockets, the shape of the ] has a high impact on the energy-to-momentum conversion, and is never perfect, and there are other sources of losses and inefficiencies (e.g. the details of the combustion in such engines). As such, the physical exhaust velocity is higher than the "effective exhaust velocity", i.e. that "velocity" suggested by the specific impulse. In any case, the momentum exchanged and the mass used to generate it ''are'' physically real measurements. Typically, rocket nozzles work better when the ambient pressure is lower, i.e. better in space than in atmosphere. Ion engines operate without a nozzle, although they have other sources of losses such that the momentum transferred is lower than the physical exhaust velocity.
==Units==


===Cars===
{| class="wikitable"
Although the car industry almost never uses specific impulse on any practical level, the measure can be defined, and makes good contrast against other engine types. Car engines breath external air to combust their fuel, and (via the wheels) react against the ground. As such, the only meaningful way to interpret "specific impulse" is as "thrust per fuelflow", although one must also specify if the force is measured at the crankshaft or at the wheels, since there are transmission losses. Such a measure corresponds to ].
|+ Imperial and SI units for various rocket motor performance measurements.
|-
!
! Specific impulse (by weight)
! Specific impulse (by mass)
! Effective exhaust velocity
! Specific fuel consumption
|-
!SI
|=X seconds
|=(9.8066 X) N•s/kg
|=(9.8066 X) m/s
|=(101,972/X) g/kN•s
|-
!Imperial units
|=X seconds
|=X lbf•s/lb
|=(32.16 X) ft/s
|=(3,600/X) lb/lbf•h
|}


===Airplanes===
By far the most common unit used for specific impulse today is the second, and this is used both in the SI world as well as where Imperial units are used. Its chief advantages are that its units and numerical value are identical everywhere, and essentially everyone understands it. Nearly all manufacturers quote their engine performance in seconds and it is also useful for specifying aircraft engine performance.<ref>http://www.grc.nasa.gov/WWW/k-12/airplane/specimp.html</ref>
In an aerodynamic context, there are similarities to both cars and rockets. Like cars, airplane engines breath outside air; unlike cars they react only against fluids flowing through the engine (including the propellers as applicable). As such, there are several possible ways to interpret "specific impulse": as thrust per fuel flow, as thrust per breathing-flow, or as thrust per "turbine-flow" (i.e. excluding air though the propeller/bypass fan). Since the air breathed isn't a direct cost, with wide engineering leeway on how much to breath, the industry traditionally chooses the "thrust per fuel flow" interpretation with its focus on cost efficiency. In this interpretation, the resulting specific impulse numbers are much higher than for rocket engines, although this comparison is essentially meaningless since the interpretations -- with or without reaction mass -- are so different.


As with all kinds of engines, there are many engineering choices and tradeoffs that affect specific impulse. Nonlinear air resistance and the engine's inability to keep a high specific impulse at a fast burn rate are limiting factors to the fuel consumption rate.
The effective exhaust velocity in units of m/s is also in reasonably common usage. For rocket engines it is reasonably intuitive, although for many rocket engines the effective exhaust speed is considerably different from the actual exhaust speed due to, for example, fuel and oxidizer that is dumped overboard after powering turbo-pumps. For air-breathing engines the effective exhaust velocity is not physically meaningful, although it can be used for comparison purposes nevertheless.<ref>http://www.qrg.northwestern.edu/projects/vss/docs/propulsion/3-what-is-specific-impulse.html</ref>


As with rocket engines, the interpretation of specific impulse as a "velocity" has no physical meaning. Since the usual interpretation excludes much of the reaction mass, the physical velocity of the reactants downstream is much lower than the I{{sub|sp}} "velocity".
The N•s/kg is not uncommonly seen, and is numerically equal to the effective exhaust velocity in m/s (from ] and the definition of the Newton.)


==General considerations==
Another equivalent unit is ]. This has units of g/kN.s or lb/lbf•h and is inversely proportional to specific impulse. Specific fuel consumption is used extensively for describing the performance of air-breathing jet engines.<ref>http://www.grc.nasa.gov/WWW/k-12/airplane/sfc.html</ref>
Specific impulse should not be confused with ], which can decrease as specific impulse increases, since propulsion systems that give high specific impulse require high energy to do so.<ref>{{cite web |url=http://www.geoffreylandis.com/laser_ion_pres.htp |title=Laser-powered Interstellar Probe (Presentation) |access-date=2013-11-16 |url-status=dead |archive-url=https://web.archive.org/web/20131002200923/http://www.geoffreylandis.com/laser_ion_pres.htp |archive-date=2 October 2013}}</ref>


Specific impulse should not be confused with total ]. Thrust is the force supplied by the engine and depends on the propellant mass flow through the engine. Specific impulse measures the thrust ''per'' propellant mass flow. Thrust and specific impulse are related by the design and propellants of the engine in question, but this relationship is tenuous: in most cases, high thrust and high specific impulse are mutually exclusive engineering goals. For example, ] bipropellant produces higher {{math|''I''<sub>sp</sub>}} (due to higher chemical energy and lower exhaust molecular mass) but lower thrust than ]/] (due to higher density and propellant flow). In many cases, propulsion systems with very high specific impulse—some ]s reach 25x-35x better {{math|''I''<sub>sp</sub>}} than chemical engines—produce correspondingly low thrust.<ref name="exploreMarsnow">{{cite web|url=http://www.exploremarsnow.org/MissionOverview.html|title=Mission Overview|publisher=exploreMarsnow|access-date=23 December 2009}}</ref>
==Specific impulse in seconds==


When calculating specific impulse, only propellant carried with the vehicle before use is counted, in the standard interpretation. This usage best corresponds to the cost of operating the vehicle. For a chemical rocket, unlike a plane or car, the propellant mass therefore would include both fuel and ]. For any vehicle, optimising for specific impulse is generally not the same as optimising for total performance or total cost. In rocketry, a heavier engine with a higher specific impulse may not be as effective in gaining altitude, distance, or velocity as a lighter engine with a lower specific impulse, especially if the latter engine possesses a higher ]. This is a significant reason for most rocket designs having multiple stages. The first stage can optimised for high thrust to effectively fight ] and air drag, while the later stages operating strictly in orbit and ] can be much easier optimised for higher specific impulse, especially for high delta-v orbits.
===General definition===
For all vehicles specific impulse (impulse per unit weight-on-Earth of propellant) in seconds can be defined by the following equation:<ref name=sutton>Rocket Propulsion Elements, 7th Edition by George P. Sutton, Oscar Biblarz</ref>


===Propellant quantity units===
:<math>F_\text{thrust} = I_\text{sp} \cdot \dot m \cdot g_0,</math>
The amount of propellant could be defined either in units of ] or ]. If mass is used, specific impulse is an ] per unit of mass, which ] shows to be equivalent to units of speed; this interpretation is commonly labeled the ''effective exhaust velocity''. If a force-based unit system is used, impulse is divided by propellant weight (weight is a measure of force), resulting in units of time. The problem with weight, as a measure of quantity, is that it depends on the acceleration applied to the propellant, which is arbitrary with no relation to the design of the engine. Historically, ] was the reference conversion between weight and mass. But since technology has progressed to the point that we can measure Earth gravity's variation across the surface, and where such differences can cause differences in practical engineering projects (not to mention science projects on other solar bodies), modern science and engineering focus on mass as the measure of quantity, so as to remove the acceleration dependence. As such, measuring specific impulse by propellant mass gives it the same meaning for a car at sea level, an airplane at cruising altitude, or a ].


No matter the choice of mass or weight, the resulting quotient of "velocity" or "time" has no physical meaning. Due to various losses in real engines, the actual exhaust velocity is different from the I{{sub|sp}} "velocity" (and for cars there isn't even a sensible definition of "actual exhaust velocity"). Rather, the specific impulse is just that: a physical momentum from a physical quantity of propellant (be that in mass or weight).
where:


The particular habit in rocketry of measuring I{{sub|sp}} in ] results from the above historical circumstances. Since metric and imperial units had in common only the unit of time, this was the most convenient way to make international comparisons. However, the choice of reference acceleration conversion, (g{{sub|0}}) is arbitrary, and as above, the interpretation in terms of time or speed has no physical meaning.
:<math>F_\text{thrust}</math> is the thrust obtained from the engine, in ]s (or ]s),
:<math>I_\text{sp}</math> is the specific impulse measured in seconds,
:<math>\dot m</math> is the ] in kg/s (lb/s), which is negative the time-rate of change of the vehicle's mass (since propellant is being expelled),
:<math>g_0</math> is the ], in m/s<sup>2</sup> (or ft/s<sup>2</sup>).


==Units==
(When working with ]s, it is conventional to divide both sides of the equation by ''g''<sub>0</sub> so that the left-hand side of the equation has units of lbs rather than expressing it in ]s.)


{| class="wikitable"
This ''I<sub>sp</sub>'' expressed in seconds is somewhat physically meaningful&mdash;if an engine's thrust could be adjusted to equal the initial weight of its propellant (measured at one ]), then ''I''<sub>sp</sub> is the duration the propellant would last.{{Citation needed|date=July 2011}}
|+ Various equivalent rocket motor performance measurements, in SI and US customary units
|-
! rowspan=2 |
! colspan=2 | Specific impulse
! rowspan=2 | Effective <br/>exhaust velocity
! rowspan=2 | Specific fuel <br/>consumption
|-
! By weight*
! By mass
|-
! SI
| = {{math|''x''}} s
| = 9.80665·{{math|''x''}} N·s/kg
| = 9.80665·{{math|''x''}} m/s
| = 101,972/{{math|''x''}} g/(kN·s)
|-
! US customary units
| = {{math|''x''}} s
| = {{math|''x''}} lbf·s/lb
| = 32.17405·{{math|''x''}} ft/s
| = 3,600/{{math|''x''}} lb/(lbf·h)
|-
| colspan="5" | *<small>as mentioned below, {{math|''x''}} s·''g<sub>0</sub>'' would be physically correct </small>
|}


The most common unit for specific impulse is the second, as values are identical regardless of whether the calculations are done in ], ], or US ] units. Nearly all manufacturers quote their engine performance in seconds, and the unit is also useful for specifying aircraft engine performance.<ref>{{Cite web|url=https://www.grc.nasa.gov/WWW/k-12/airplane/specimp.html|title=Specific Impulse|website=www.grc.nasa.gov}}</ref>
The advantage of this formulation is that it may be used for rockets, where all the reaction mass is carried on board, as well as aeroplanes, where most of the reaction mass is taken from the atmosphere. In addition, it gives a result that is independent of units used (provided the unit of time used is the second).


The use of ] to specify effective exhaust velocity is also reasonably common. The unit is intuitive when describing rocket engines, although the effective exhaust speed of the engines may be significantly different from the actual exhaust speed, especially in ] engines. For ]s, the effective exhaust velocity is not physically meaningful, although it can be used for comparison purposes.<ref>{{Cite web|url=https://www.qrg.northwestern.edu/projects/vss/docs/propulsion/3-what-is-specific-impulse.html|title=What is specific impulse?|website=www.qrg.northwestern.edu}}</ref>
]


Metres per second are numerically equivalent to newton-seconds per kg (N·s/kg), and SI measurements of specific impulse can be written in terms of either units interchangeably. This unit highlights the definition of specific impulse as ] per unit mass of propellant.
===Rocketry===
In rocketry, where the only reaction mass is the propellant, an equivalent way of calculating the specific impulse in seconds is also frequently used. In this sense, specific impulse is defined as the thrust integrated over time per unit ]-on-Earth of the propellant:<ref name="SINasa"/>


] is inversely proportional to specific impulse and has units of g/(kN·s) or lb/(lbf·h). Specific fuel consumption is used extensively for describing the performance of air-breathing jet engines.<ref>{{Cite web|title=Specific Fuel Consumption|url=https://www.grc.nasa.gov/WWW/k-12/airplane/sfc.html|access-date=2021-05-13|website=www.grc.nasa.gov}}</ref>
:<math>I_{\rm sp}=\frac{v_{\rm e}}{g_{\rm 0}}</math><ref name="SINasa"/>


===Specific impulse in seconds===
where
{{Refimprove section|date=August 2019}}
Specific impulse, measured in seconds, can be thought of as how many seconds one kilogram of fuel can produce one kilogram of thrust. Or, more precisely, how many seconds a given propellant, when paired with a given engine, can accelerate its own initial mass at 1&nbsp;g. The longer it can accelerate its own mass, the more delta-V it delivers to the whole system.


In other words, given a particular engine and a mass of a particular propellant, specific impulse measures for how long a time that engine can exert a continuous force (thrust) until fully burning that mass of propellant. A given mass of a more energy-dense propellant can burn for a longer duration than some less energy-dense propellant made to exert the same force while burning in an engine. Different engine designs burning the same propellant may not be equally efficient at directing their propellant's energy into effective thrust.
''I''<sub>sp</sub> is the specific impulse measured in seconds


For all vehicles, specific impulse (impulse per unit weight-on-Earth of propellant) in seconds can be defined by the following equation:<ref name=sutton>Rocket Propulsion Elements, 7th Edition by George P. Sutton, Oscar Biblarz</ref>
<math>v_{\rm e}</math> is the average exhaust speed along the axis of the engine (in ft/s or m/s)


<math display="block">F_\text{thrust} = g_0 \cdot I_\text{sp} \cdot \dot m,</math>
''g<sub>0</sub>'' is the acceleration at the Earth's surface (in ft/s<sup>2</sup> or m/s<sup>2</sup>).


where:
In rockets, due to atmospheric effects, the specific impulse varies with altitude, reaching a maximum in a vacuum. This is because the exhaust velocity isn't simply a function of the chamber pressure, but is a function of the difference between the interior and exterior of the combustion chamber.
It is therefore important to note if the specific impulse is vacuum or lower sea level. Values are usually indicated with or near the units of specific impulse (e.g. 'sl', 'vac').


*<math>F_\text{thrust}</math> is the thrust obtained from the engine (]s or ]),
==Specific impulse as a speed (effective exhaust velocity)==
*<math>g_0</math> is the ], which is nominally the gravity at Earth's surface (m/s<sup>2</sup> or ft/s<sup>2</sup>),
Because of the geocentric factor of ''g''<sub>0</sub> in the equation for specific impulse, many prefer to define the specific impulse of a rocket (in particular) in terms of thrust per unit mass flow of propellant (instead of per unit weight flow). This is an equally valid (and in some ways somewhat simpler) way of defining the effectiveness of a rocket propellant. For a rocket, the specific impulse defined in this way is simply the effective exhaust velocity relative to the rocket, v<sub>e</sub>. The two definitions of specific impulse are proportional to one another, and related to each other by:
*<math>I_\text{sp}</math> is the specific impulse measured (seconds),
*<math>\dot m</math> is the ] of the expended propellant (kg/s or ]s/s)


''I''<sub>sp</sub> in seconds is the amount of time a rocket engine can generate thrust, given a quantity of propellant whose weight is equal to the engine's thrust.
:<math>v_{\rm e} = g_0 I_{\rm sp} \,</math>


The advantage of this formulation is that it may be used for rockets, where all the reaction mass is carried on board, as well as airplanes, where most of the reaction mass is taken from the atmosphere. In addition, giving the result as a unit of time makes the result easily comparable between calculations in SI units, imperial units, US customary units or other unit framework.
where


])]]
:<math>I_{\rm sp} \,</math> - is the specific impulse in seconds


====Imperial units conversion====
:<math>v_{\rm e} \,</math> - is the specific impulse measured in ], which is the same as the effective exhaust velocity measured in m/s (or ft/s if g is in ft/s<sup>2</sup>)
The ] ] is more commonly used than the slug, and when using pounds per second for mass flow rate, it is more convenient to express standard gravity as 1 pound-force per pound-mass. Note that this is equivalent to 32.17405 ft/s2, but expressed in more convenient units. This gives:


<math display="block">F_\text{thrust} = I_\text{sp} \cdot \dot m \cdot \left(1 \mathrm{\frac{lbf}{lbm}} \right).</math>
:<math>g_0 \,</math> - is the acceleration due to gravity at the Earth's surface, 9.81 m/s<sup>2</sup> (in ] units 32.2 ft/s<sup>2</sup>).


====Rocketry====
This equation is also valid for air-breathing jet engines, but is rarely used in practice.
In rocketry, the only reaction mass is the propellant, so the specific impulse is calculated using an alternative method, giving results with units of seconds. Specific impulse is defined as the thrust integrated over time per unit ]-on-Earth of the propellant:<ref name="SINasa">{{cite web|url=http://www.grc.nasa.gov/WWW/K-12/airplane/specimp.html|title=Specific impulse|last=Benson|first=Tom|date=11 July 2008|publisher=]|access-date=22 December 2009}}</ref>


<math display="block">I_\text{sp} = \frac{v_\text{e}}{g_0},</math>
(Note that different symbols are sometimes used; for example, ''c'' is also sometimes seen for exhaust velocity. While the symbol <math>I_{sp}</math> might logically be used for specific impulse in units of N•s/kg, to avoid confusion it is desirable to reserve this for specific impulse measured in seconds.)

It is related to the ], or forward force on the rocket by the equation:

:<math>\mathrm{F_{\rm thrust}}=v_{\rm e} \cdot \dot m \,</math><ref></ref>


where where


:<math>\dot m</math> is the propellant mass flow rate, which is the rate of decrease of the vehicle's mass *<math>I_\text{sp}</math> is the specific impulse measured in seconds,
*<math>v_\text{e}</math> is the average exhaust speed along the axis of the engine (in m/s or ft/s),
*<math>g_0</math> is the ] (in m/s<sup>2</sup> or ft/s<sup>2</sup>).


In rockets, due to atmospheric effects, the specific impulse varies with altitude, reaching a maximum in a vacuum. This is because the exhaust velocity isn't simply a function of the chamber pressure, but is ]. Values are usually given for operation at sea level ("sl") or in a vacuum ("vac").
A rocket must carry all its fuel with it, so the mass of the unburned fuel must be accelerated along with the rocket itself. Minimizing the mass of fuel required to achieve a given push is crucial to building effective rockets. The ] shows that for a rocket with a given empty mass and a given amount of fuel, the total change in ] it can accomplish is proportional to the effective exhaust velocity.


===Specific impulse as effective exhaust velocity===
A spacecraft without propulsion follows an orbit determined by the gravitational field. Deviations from the corresponding velocity pattern (these are called ]) are achieved by sending exhaust mass in the direction opposite to that of the desired velocity change.
{{Refimprove section|date=August 2019}}
Because of the geocentric factor of ''g''<sub>0</sub> in the equation for specific impulse, many prefer an alternative definition. The specific impulse of a rocket can be defined in terms of thrust per unit mass flow of propellant. This is an equally valid (and in some ways somewhat simpler) way of defining the effectiveness of a rocket propellant. For a rocket, the specific impulse defined in this way is simply the effective exhaust velocity relative to the rocket, ''v''<sub>e</sub>. "In actual rocket nozzles, the exhaust velocity is not really uniform over the entire exit cross section and such velocity profiles are difficult to measure accurately. A uniform axial velocity, ''v''<sub>e</sub>, is assumed for all calculations which employ one-dimensional problem descriptions. This effective exhaust velocity represents an average or mass equivalent velocity at which propellant is being ejected from the rocket vehicle."<ref>{{cite book|author=George P. Sutton & Oscar Biblarz|title=Rocket Propulsion Elements|url=https://books.google.com/books?id=2qehDQAAQBAJ|year=2016|publisher=John Wiley & Sons| isbn=978-1-118-75388-0|page=27}}</ref> The two definitions of specific impulse are proportional to one another, and related to each other by:
<math display="block">v_\text{e} = g_0 \cdot I_\text{sp},</math>
where
*<math>I_\text{sp}</math> is the specific impulse in seconds,
*<math>v_\text{e}</math> is the specific impulse measured in ], which is the same as the effective exhaust velocity measured in m/s (or ft/s if g is in ft/s<sup>2</sup>),
*<math>g_0</math> is the ], 9.80665 m/s<sup>2</sup> (in ] 32.174 ft/s<sup>2</sup>).


This equation is also valid for air-breathing jet engines, but is rarely used in practice.
===Actual exhaust speed versus effective exhaust speed===


(Note that different symbols are sometimes used; for example, ''c'' is also sometimes seen for exhaust velocity. While the symbol <math>I_\text{sp}</math> might logically be used for specific impulse in units of (N·s{{sup|3}})/(m·kg); to avoid confusion, it is desirable to reserve this for specific impulse measured in seconds.)
Note that '''effective''' exhaust velocity and '''actual''' exhaust velocity can be significantly different, for example when a rocket is run within the atmosphere, atmospheric pressure on the outside of the engine causes a retarding force that reduces the specific impulse and the effective exhaust velocity goes down, whereas the actual exhaust velocity is largely unaffected. Also, sometimes rocket engines have a separate nozzle for the turbo-pump turbine gas, and then calculating the effective exhaust velocity requires averaging the two mass flows as well as accounting for any atmospheric pressure.{{Citation needed|date=July 2011}}


It is related to the ], or forward force on the rocket by the equation:<ref>{{cite book|author=Thomas A. Ward | title=Aerospace Propulsion Systems|url=https://books.google.com/books?id=KEPgEgX2BEEC&pg=PA68|year=2010|publisher=John Wiley & Sons |isbn=978-0-470-82497-9|page=68}}</ref>
For air-breathing jet engines, particularly ]s, the actual exhaust velocity and the effective exhaust velocity are different by orders of magnitude. This is because a good deal of additional momentum is obtained by using air as reaction mass. This allows for a better match between the airspeed and the exhaust speed which saves energy/propellant and enormously increases the effective exhaust velocity while reducing the actual exhaust velocity.{{Citation needed|date=July 2011}}
<math display="block">F_\text{thrust} = v_\text{e} \cdot \dot m,</math>
where <math>\dot m</math> is the propellant mass flow rate, which is the rate of decrease of the vehicle's mass.


A rocket must carry all its propellant with it, so the mass of the unburned propellant must be accelerated along with the rocket itself. Minimizing the mass of propellant required to achieve a given change in velocity is crucial to building effective rockets. The ] shows that for a rocket with a given empty mass and a given amount of propellant, the total change in ] it can accomplish is proportional to the effective exhaust velocity.
==Energy efficiency==


A spacecraft without propulsion follows an orbit determined by its trajectory and any gravitational field. Deviations from the corresponding velocity pattern (these are called ]) are achieved by sending exhaust mass in the direction opposite to that of the desired velocity change.
===Rockets===
For rockets and rocket-like engines such as ion-drives a higher <math>I_{sp}</math> implies lower energy efficiency: the power needed to run the engine is simply:


===Actual exhaust speed versus effective exhaust speed===
:<math>\frac {dm} {dt} \frac { v_e^2 } {2}</math>


When an engine is run within the atmosphere, the exhaust velocity is reduced by atmospheric pressure, in turn reducing specific impulse. This is a reduction in the effective exhaust velocity, versus the actual exhaust velocity achieved in vacuum conditions. In the case of ] rocket engines, more than one exhaust gas stream is present as ] exhaust gas exits through a separate nozzle. Calculating the effective exhaust velocity requires averaging the two mass flows as well as accounting for any atmospheric pressure.<ref>{{Cite web |title=Rocket Thrust Equations |url=https://www.grc.nasa.gov/WWW/k-12/airplane/rktthsum.html |archive-url=http://web.archive.org/web/20241109090800/https://www.grc.nasa.gov/www/k-12/airplane/rktthsum.html |archive-date=2024-11-09 |access-date=2024-12-11 |website=www.grc.nasa.gov}}</ref>
where v<sub>e</sub> is the actual jet velocity.


For air-breathing jet engines, particularly ]s, the actual exhaust velocity and the effective exhaust velocity are different by orders of magnitude. This happens for several reasons. First, a good deal of additional momentum is obtained by using air as reaction mass, such that combustion products in the exhaust have more mass than the burned fuel. Next, inert gases in the atmosphere absorb heat from combustion, and through the resulting expansion provide additional thrust. Lastly, for turbofans and other designs there is even more thrust created by pushing against intake air which never sees combustion directly. These all combine to allow a better match between the airspeed and the exhaust speed, which saves energy/propellant and enormously increases the ''effective'' exhaust velocity while reducing the ''actual'' exhaust velocity.<ref>{{Cite journal |date=2023-01-23 |title=Research on Efficient Heat Transfer for Air Breathing Electric Propulsion |url=https://doi.org/10.2514/6.2023-0450.vid |access-date=2024-12-11 |website=doi.org|doi=10.2514/6.2023-0450.vid }}</ref> Again, this is because the mass of the air is not counted in the specific impulse calculation, thus attributing ''all'' of the thrust momentum to the mass of the fuel component of the exhaust, and omitting the reaction mass, inert gas, and effect of driven fans on overall engine efficiency from consideration.
whereas from momentum considerations the thrust generated is:


Essentially, the momentum of engine exhaust includes a lot more than just fuel, but specific impulse calculation ignores everything but the fuel. Even though the ''effective'' exhaust velocity for an air-breathing engine seems nonsensical in the context of actual exhaust velocity, this is still useful for comparing absolute ] of different engines.
:<math>\frac {dm} {dt} v_e</math>


===Density specific impulse===
Dividing the power by the thrust to obtain the specific power requirements we get:


A related measure, the '''density specific impulse''', sometimes also referred to as '''Density Impulse''' and usually abbreviated as {{math|''I''<sub>s</sub>''d''}} is the product of the average specific gravity of a given propellant mixture and the specific impulse.<ref>{{cite encyclopedia |url=https://encyclopedia2.thefreedictionary.com/density+specific+impulse |website=encyclopedia2.thefreedictionary.com |title=Density specific impulse |access-date=20 September 2022}}</ref> While less important than the specific impulse, it is an important measure in launch vehicle design, as a low specific impulse implies that bigger tanks will be required to store the propellant, which in turn will have a detrimental effect on the launch vehicle's ].<ref>{{cite web |title=Rocket Propellants |url=http://www.braeunig.us/space/propel.htm |website=braeunig.us |access-date=20 September 2022}}</ref>
:<math>\frac {v_e} {2}</math>


===Specific fuel consumption===
Hence the power needed is proportional to the exhaust velocity, with higher velocities needing higher power for the same thrust, causing less energy efficiency per unit thrust.
Specific impulse is inversely proportional to ] (SFC) by the relationship {{math|1=''I''<sub>sp</sub> = 1/(''g<sub>o</sub>''·SFC)}} for SFC in kg/(N·s) and {{math|1=''I''<sub>sp</sub> = 3600/SFC}} for SFC in lb/(lbf·hr).

However, the total energy for a mission depends on total propellant use, as well as how much energy is needed per unit of propellant. For low exhaust velocity with respect to the mission delta-v, enormous amounts of reaction mass is needed. In fact a very low exhaust velocity is not energy efficient at all for this reason; but it turns out that neither are very high exhaust velocities.

Theoretically, for a given ], in space, among all fixed values for the exhaust speed the value <math>v_\text{e}=0.6275 \Delta v</math> is the most energy efficient for a specified (fixed) final mass, see ].

However, a variable exhaust speed can be more energy efficient still. For example, if a rocket is accelerated from some positive initial speed using an exhaust speed equal to the speed of the rocket no energy is lost as kinetic energy of reaction mass, since it becomes stationary.<ref>Note that this limits the speed of the rocket to the maximum exhaust speed.</ref> (Theoretically, by making this initial speed low and using another method of obtaining this small speed, the energy efficiency approaches 100%, but requires a large initial mass.) In this case the rocket keeps the same ], so its speed is inversely proportional to its remaining mass. During such a flight the kinetic energy of the rocket is proportional to its speed and, correspondingly, inversely proportional to its remaining mass. The power needed per unit acceleration is constant throughout the flight; the reaction mass to be expelled per unit time to produce a given acceleration is proportional to the square of the rocket's remaining mass.

Also it is advantageous to expel reaction mass at a location where the ] is low, see ].

===Air breathing===
Air-breathing engines such as ]s increase the momentum generated from their propellant by using it to power the acceleration of inert air rearwards. It turns out that the amount of energy needed to generate a particular amount of thrust is inversely proportional to the amount of air propelled rearwards, thus increasing the mass of air (as with a ]) both improves energy efficiency as well as <math>I_{sp}</math>.


==Examples== ==Examples==
{{main list|Spacecraft propulsion#Table of methods}}
{{Thrust engine efficiency}}
{{Specific impulse examples}} {{Specific impulse examples}}
:''For a more complete list see: ]''


An example of a specific impulse measured in time is 453 ]s, which is equivalent to an ] of 4,440 ], for the ]s when operating in a vacuum.<ref>http://www.astronautix.com/engines/ssme.htm</ref> An air-breathing jet engine typically has a much larger specific impulse than a rocket; for example a ] jet engine may have a specific impulse of 6,000 seconds or more at sea level whereas a rocket would be around 200–400 seconds.<ref>http://web.mit.edu/16.unified/www/SPRING/propulsion/notes/node85.html</ref> An example of a specific impulse measured in time is 453&nbsp;seconds, which is equivalent to an ] of {{cvt|4.440|km/s|ft/s}}, for the ] engines when operating in a vacuum.<ref>{{Cite web|url=http://www.astronautix.com/engines/ssme.htm|title=SSME|website=www.astronautix.com|url-status=dead|archive-url=https://web.archive.org/web/20160303190701/http://www.astronautix.com/engines/ssme.htm|archive-date=March 3, 2016}}{{cbignore|bot=medic}}</ref> An air-breathing jet engine typically has a much larger specific impulse than a rocket; for example a ] jet engine may have a specific impulse of 6,000&nbsp;seconds or more at sea level whereas a rocket would be between 200 and 400&nbsp;seconds.<ref>{{Cite web|url=http://web.mit.edu/16.unified/www/SPRING/propulsion/notes/node85.html|title=11.6 Performance of Jet Engines|website=web.mit.edu}}</ref>


An air-breathing engine is thus much more propellant efficient than a rocket engine, because the actual exhaust speed is much lower, the air provides an oxidizer, and air is used as reaction mass. Since the physical exhaust velocity is lower, the kinetic energy the exhaust carries away is lower and thus the jet engine uses far less energy to generate thrust (at subsonic speeds).<ref>http://www.dunnspace.com/isp.htm</ref> While the '''actual''' exhaust velocity is lower for air-breathing engines, the '''effective''' exhaust velocity is very high for jet engines. This is because the effective exhaust velocity calculation essentially assumes that the propellant is providing all the thrust, and hence is not physically meaningful for air-breathing engines; nevertheless, it is useful for comparison with other types of engines.<ref>http://www.britannica.com/EBchecked/topic/198045/effective-exhaust-velocity</ref> An air-breathing engine is thus much more propellant efficient than a rocket engine, because the air serves as reaction mass and oxidizer for combustion which does not have to be carried as propellant, and the actual exhaust speed is much lower, so the kinetic energy the exhaust carries away is lower and thus the jet engine uses far less energy to generate thrust.<ref>{{cite web|last=Dunn|first=Bruce P.|date=2001|title=Dunn's readme|url=http://www.dunnspace.com/isp.htm|url-status=dead|archive-url=https://web.archive.org/web/20131020061623/http://www.dunnspace.com/isp.htm|archive-date=20 October 2013|access-date=2014-07-12}}</ref> While the ''actual'' exhaust velocity is lower for air-breathing engines, the ''effective'' exhaust velocity is very high for jet engines. This is because the effective exhaust velocity calculation assumes that the carried propellant is providing all the reaction mass and all the thrust. Hence effective exhaust velocity is not physically meaningful for air-breathing engines; nevertheless, it is useful for comparison with other types of engines.<ref>{{Cite web|url=https://www.britannica.com/technology/effective-exhaust-velocity|title=Effective exhaust velocity &#124; engineering|website=Encyclopedia Britannica}}</ref>


The highest specific impulse for a chemical propellant ever test-fired in a rocket engine was 542 seconds (5,320&nbsp;m/s) with a ] of ], ], and ]. However, this combination is impractical; see ].<ref>ARBIT, H. A., CLAPP, S. D., DICKERSON, R. A., NAGAI, C. K., AMERICAN INST OF AERONAUTICS AND ASTRONAUTICS, PROPULSION JOINT SPECIALIST CONFERENCE, 4TH, CLEVELAND, OHIO, June 10–14, 1968.</ref> The highest specific impulse for a chemical propellant ever test-fired in a rocket engine was {{convert|542|isp}} with a ] of ], ], and ]. However, this combination is impractical. Lithium and fluorine are both extremely corrosive, lithium ignites on contact with air, fluorine ignites on contact with most fuels, and hydrogen, while not hypergolic, is an explosive hazard. Fluorine and the hydrogen fluoride (HF) in the exhaust are very toxic, which damages the environment, makes work around the launch pad difficult, and makes getting a launch license that much more difficult. The rocket exhaust is also ionized, which would interfere with radio communication with the rocket.<ref>{{Cite web|url=https://space.stackexchange.com/questions/19852/where-is-the-lithium-fluorine-hydrogen-tripropellant-currently|title=fuel - Where is the Lithium-Fluorine-Hydrogen tripropellant currently?|website=Space Exploration Stack Exchange}}</ref><ref>{{Cite book|chapter-url=https://dx.doi.org/10.2514/6.1968-618|doi = 10.2514/6.1968-618|chapter = Investigation of the lithium-fluorine-hydrogen tripropellant system|title = 4th Propulsion Joint Specialist Conference|year = 1968|last1 = Arbit|first1 = H.|last2 = Clapp|first2 = S.|last3 = Nagai|first3 = C.}}</ref><ref>ARBIT, H. A., CLAPP, S. D., NAGAI, C. K., NASA, 1 May 1970.</ref>


] engines differ from conventional rocket engines in that thrust is created strictly through thermodynamic phenomena, with no chemical reaction.<ref>http://trajectory.grc.nasa.gov/projects/ntp/index.shtml</ref> The nuclear rocket typically operates by passing hydrogen gas through a superheated nuclear core. Testing in the 1960s yielded specific impulses of about 850 seconds (8,340&nbsp;m/s), about twice that of the Space Shuttle engines. ] engines differ from conventional rocket engines in that energy is supplied to the propellants by an external nuclear heat source instead of the ].<ref>{{Cite web |url=http://trajectory.grc.nasa.gov/projects/ntp/index.shtml |title=Space Propulsion and Mission Analysis Office |access-date=20 July 2011 |archive-date=12 April 2011 |archive-url=https://web.archive.org/web/20110412093255/http://trajectory.grc.nasa.gov/projects/ntp/index.shtml |url-status=dead }}</ref> The nuclear rocket typically operates by passing liquid hydrogen gas through an operating nuclear reactor. Testing in the 1960s yielded specific impulses of about 850 seconds (8,340&nbsp;m/s), about twice that of the Space Shuttle engines.<ref>{{Citation|last=National Aeronautics and Space Administration|title=Nuclear Propulsion in Space|date=5 January 2017 |url=https://www.youtube.com/watch?v=eDNX65d-FBY |archive-url=https://ghostarchive.org/varchive/youtube/20211211/eDNX65d-FBY| archive-date=2021-12-11 |url-status=live|language=en|access-date=2021-02-24}}{{cbignore}}</ref>


A variety of other non-rocket propulsion methods, such as ]s, give much higher specific impulse but with much lower thrust; for example the ] on the ] satellite has a specific impulse of 1,640 s (16,100&nbsp;m/s) but a maximum thrust of only 68 millinewtons.<ref>http://www.mendeley.com/research/characterization-of-a-high-specific-impulse-xenon-hall-effect-thruster/</ref> The ] (VASIMR) engine currently in development will theoretically yield 10,000−300,000&nbsp;m/s but will require a large electricity source and a great deal of heavy machinery to confine even relatively diffuse plasmas, and so will be unusable for high-thrust applications such as launch from planetary surfaces.<ref>http://www.nasa.gov/vision/space/travelinginspace/future_propulsion.html</ref> A variety of other rocket propulsion methods, such as ]s, give much higher specific impulse but with much lower thrust; for example the ] on the ] satellite has a specific impulse of {{cvt|1640|isp}} but a maximum thrust of only {{cvt|68|mN|lbf}}.<ref>{{Cite web |url=http://www.mendeley.com/research/characterization-of-a-high-specific-impulse-xenon-hall-effect-thruster/ |title=Characterization of a High Specific Impulse Xenon Hall Effect Thruster &#124; Mendeley |access-date=20 July 2011 |archive-date=24 March 2012 |archive-url=https://web.archive.org/web/20120324114628/http://www.mendeley.com/research/characterization-of-a-high-specific-impulse-xenon-hall-effect-thruster/ |url-status=dead }}</ref> The ] (VASIMR) engine currently in development will theoretically yield {{cvt|20|to|300|km/s|ft/s}}, and a maximum thrust of {{cvt|5.7|N|lbf}}.<ref>{{Cite web|last=Ad Astra|date=November 23, 2010|title=VASIMR® VX-200 MEETS FULL POWER EFFICIENCY MILESTONE|url=http://www.adastrarocket.com/AdAstra%20Release%2023Nov2010final.pdf|url-status=dead|access-date=23 June 2014|archive-date=30 October 2012|archive-url=https://web.archive.org/web/20121030193000/http://www.adastrarocket.com/AdAstra%20Release%2023Nov2010final.pdf}}</ref>

===Larger engines===
Here are some example numbers for larger jet and rocket engines:
{{Thrust engine efficiency}}

===Model rocketry===
Specific impulse is also used to measure performance in model rocket motors. Following are some of Estes' claimed values for specific impulses for several of their rocket motors:<ref>Estes 2011 Catalog www.acsupplyco.com/estes/estes_cat_2011.pdf</ref> ] is a large, well-known American seller of model rocket components. The specific impulse for these model rocket motors is much lower than for many other rocket motors because the manufacturer uses black powder propellant and emphasizes safety rather than maximum performance. The burn rate and hence chamber pressure and maximum thrust of model rocket motors is also tightly controlled.
{| class="wikitable"
|-
|+ align="bottom" style="caption-side: bottom" | Specific impulses for several commercially available Estes rocket motors.
! rowspan="1"|Engine||Total impulse (Ns)||Fuel weight (N)||Specific impulse (s)
|-----
| Estes A10-3T ||2.5||0.0370||67.49
|-----
| Estes A8-3 ||2.5||0.0306||81.76
|-----
| Estes B4-2 ||5.0||0.0816||61.25
|-----
| Estes B6-4 ||5.0||0.0612||81.76
|-----
| Estes C6-3 ||10||0.1223||81.76
|-----
| Estes C11-5 ||10||0.1078||92.76
|-----
| Estes D12-3 ||20||0.2443||81.86
|-----
| Estes E9-6||30||0.3508||85.51
|}


==See also== ==See also==
{{div col}} {{div col|colwidth=30em}}
*] * ]
*] * ]
*] * ]
*] * ]
*] * ]
* ]
*] - fuel consumption per unit thrust
* ]—fuel consumption per unit thrust
*] - thrust per unit of air for a duct engine
* ]—thrust per unit of air for a duct engine
*]
*] * ]
*] * ]
*] * ]
* ]
*]
* ]
{{div col end}} {{div col end}}

==Notes==
{{reflist|group=note}}


==References== ==References==
{{Reflist|2}} {{Reflist}}
{{reflist|group=lower-alpha}}


==External links== ==External links==
* *
* *

{{Use dmy dates|date=July 2011}}


{{DEFAULTSORT:Specific Impulse}} {{DEFAULTSORT:Specific Impulse}}

<!--Categories-->
] ]
] ]

Latest revision as of 15:18, 21 December 2024

Change in velocity per amount of fuel

Specific impulse (usually abbreviated Isp) is a measure of how efficiently a reaction mass engine, such as a rocket using propellant or a jet engine using fuel, generates thrust. In general, this is a ratio of the impulse, i.e. change in momentum, per mass of propellant. This is equivalent to "thrust per massflow". The resulting unit is equivalent to velocity, although it doesn't represent any physical velocity (see below); it is more properly thought of in terms of momentum per mass, since this represents a physical momentum and physical mass.

The practical meaning of the measurement varies with different types of engines. Car engines consume onboard fuel, breathe environmental air to burn the fuel, and react (through the tires) against the ground beneath them. In this case, the only sensible interpretation is momentum per fuel burned. Chemical rocket engines, by contrast, carry aboard all of their combustion ingredients and reaction mass, so the only practical measure is momentum per reaction mass. Airplane engines are in the middle, as they only react against airflow through the engine, but some of this reaction mass (and combustion ingredients) is breathed rather than carried aboard. As such, "specific impulse" could be taken to mean either "per reaction mass", as with a rocket, or "per fuel burned" as with cars. The latter is the traditional and common choice. In sum, specific impulse isn't practically comparable between different types of engines.

In any case, specific impulse can be taken as a measure of efficiency. In cars and planes, it typically corresponds with fuel mileage; in rocketry, it corresponds to the achievable delta-v, which is the typical way to measure changes between orbits.

Rocketry traditionally uses a "bizarre" choice of units: rather than speaking of momentum-per-mass, or velocity, the rocket industry typically converts units of velocity to units of time by dividing by a standard reference acceleration, that being standard gravity g0. This is a historical result of competing units, imperial units vs metric units. They shared a common unit of time (seconds) but not common units of distance or mass, so this conversion by reference to g0 became a standard way to make international comparisons. This choice of reference conversion is arbitrary and the resulting units of time have no physical meaning. The only physical quantities are the momentum change and the mass used to achieve it.

Propulsion systems

Rockets

For any chemical rocket engine, the momentum transfer efficiency depends heavily on the effectiveness of the nozzle; the nozzle is the primary means of converting reactant energy (e.g. thermal or pressure energy) into a flow of momentum all directed the same way. Therefore, nozzle shape and effectiveness has a great impact on total momentum transfer from the reaction mass to the rocket.

Efficiency of conversion of input energy to reactant energy also matters; be that thermal energy in combustion engines or electrical energy in ion engines, the engineering involved in converting such energy to outbound momentum can have high impact on specific impulse. Specific impulse in turn has deep impacts on the achievable delta-v and associated orbits achievable, and (by the rocket equation) mass fraction required to achieve a given delta-v. Optimizing the tradeoffs between mass fraction and specific impulse is one of the fundamental engineering challenges in rocketry.

Although the specific impulse has units equivalent to velocity, it almost never corresponds to any physical velocity. In chemical and cold gas rockets, the shape of the nozzle has a high impact on the energy-to-momentum conversion, and is never perfect, and there are other sources of losses and inefficiencies (e.g. the details of the combustion in such engines). As such, the physical exhaust velocity is higher than the "effective exhaust velocity", i.e. that "velocity" suggested by the specific impulse. In any case, the momentum exchanged and the mass used to generate it are physically real measurements. Typically, rocket nozzles work better when the ambient pressure is lower, i.e. better in space than in atmosphere. Ion engines operate without a nozzle, although they have other sources of losses such that the momentum transferred is lower than the physical exhaust velocity.

Cars

Although the car industry almost never uses specific impulse on any practical level, the measure can be defined, and makes good contrast against other engine types. Car engines breath external air to combust their fuel, and (via the wheels) react against the ground. As such, the only meaningful way to interpret "specific impulse" is as "thrust per fuelflow", although one must also specify if the force is measured at the crankshaft or at the wheels, since there are transmission losses. Such a measure corresponds to fuel mileage.

Airplanes

In an aerodynamic context, there are similarities to both cars and rockets. Like cars, airplane engines breath outside air; unlike cars they react only against fluids flowing through the engine (including the propellers as applicable). As such, there are several possible ways to interpret "specific impulse": as thrust per fuel flow, as thrust per breathing-flow, or as thrust per "turbine-flow" (i.e. excluding air though the propeller/bypass fan). Since the air breathed isn't a direct cost, with wide engineering leeway on how much to breath, the industry traditionally chooses the "thrust per fuel flow" interpretation with its focus on cost efficiency. In this interpretation, the resulting specific impulse numbers are much higher than for rocket engines, although this comparison is essentially meaningless since the interpretations -- with or without reaction mass -- are so different.

As with all kinds of engines, there are many engineering choices and tradeoffs that affect specific impulse. Nonlinear air resistance and the engine's inability to keep a high specific impulse at a fast burn rate are limiting factors to the fuel consumption rate.

As with rocket engines, the interpretation of specific impulse as a "velocity" has no physical meaning. Since the usual interpretation excludes much of the reaction mass, the physical velocity of the reactants downstream is much lower than the Isp "velocity".

General considerations

Specific impulse should not be confused with energy efficiency, which can decrease as specific impulse increases, since propulsion systems that give high specific impulse require high energy to do so.

Specific impulse should not be confused with total thrust. Thrust is the force supplied by the engine and depends on the propellant mass flow through the engine. Specific impulse measures the thrust per propellant mass flow. Thrust and specific impulse are related by the design and propellants of the engine in question, but this relationship is tenuous: in most cases, high thrust and high specific impulse are mutually exclusive engineering goals. For example, LH2/LO2 bipropellant produces higher Isp (due to higher chemical energy and lower exhaust molecular mass) but lower thrust than RP-1/LO2 (due to higher density and propellant flow). In many cases, propulsion systems with very high specific impulse—some ion thrusters reach 25x-35x better Isp than chemical engines—produce correspondingly low thrust.

When calculating specific impulse, only propellant carried with the vehicle before use is counted, in the standard interpretation. This usage best corresponds to the cost of operating the vehicle. For a chemical rocket, unlike a plane or car, the propellant mass therefore would include both fuel and oxidizer. For any vehicle, optimising for specific impulse is generally not the same as optimising for total performance or total cost. In rocketry, a heavier engine with a higher specific impulse may not be as effective in gaining altitude, distance, or velocity as a lighter engine with a lower specific impulse, especially if the latter engine possesses a higher thrust-to-weight ratio. This is a significant reason for most rocket designs having multiple stages. The first stage can optimised for high thrust to effectively fight gravity drag and air drag, while the later stages operating strictly in orbit and in vacuum can be much easier optimised for higher specific impulse, especially for high delta-v orbits.

Propellant quantity units

The amount of propellant could be defined either in units of mass or weight. If mass is used, specific impulse is an impulse per unit of mass, which dimensional analysis shows to be equivalent to units of speed; this interpretation is commonly labeled the effective exhaust velocity. If a force-based unit system is used, impulse is divided by propellant weight (weight is a measure of force), resulting in units of time. The problem with weight, as a measure of quantity, is that it depends on the acceleration applied to the propellant, which is arbitrary with no relation to the design of the engine. Historically, standard gravity was the reference conversion between weight and mass. But since technology has progressed to the point that we can measure Earth gravity's variation across the surface, and where such differences can cause differences in practical engineering projects (not to mention science projects on other solar bodies), modern science and engineering focus on mass as the measure of quantity, so as to remove the acceleration dependence. As such, measuring specific impulse by propellant mass gives it the same meaning for a car at sea level, an airplane at cruising altitude, or a helicopter on Mars.

No matter the choice of mass or weight, the resulting quotient of "velocity" or "time" has no physical meaning. Due to various losses in real engines, the actual exhaust velocity is different from the Isp "velocity" (and for cars there isn't even a sensible definition of "actual exhaust velocity"). Rather, the specific impulse is just that: a physical momentum from a physical quantity of propellant (be that in mass or weight).

The particular habit in rocketry of measuring Isp in seconds results from the above historical circumstances. Since metric and imperial units had in common only the unit of time, this was the most convenient way to make international comparisons. However, the choice of reference acceleration conversion, (g0) is arbitrary, and as above, the interpretation in terms of time or speed has no physical meaning.

Units

Various equivalent rocket motor performance measurements, in SI and US customary units
Specific impulse Effective
exhaust velocity
Specific fuel
consumption
By weight* By mass
SI = x s = 9.80665·x N·s/kg = 9.80665·x m/s = 101,972/x g/(kN·s)
US customary units = x s = x lbf·s/lb = 32.17405·x ft/s = 3,600/x lb/(lbf·h)
*as mentioned below, xg0 would be physically correct

The most common unit for specific impulse is the second, as values are identical regardless of whether the calculations are done in SI, imperial, or US customary units. Nearly all manufacturers quote their engine performance in seconds, and the unit is also useful for specifying aircraft engine performance.

The use of metres per second to specify effective exhaust velocity is also reasonably common. The unit is intuitive when describing rocket engines, although the effective exhaust speed of the engines may be significantly different from the actual exhaust speed, especially in gas-generator cycle engines. For airbreathing jet engines, the effective exhaust velocity is not physically meaningful, although it can be used for comparison purposes.

Metres per second are numerically equivalent to newton-seconds per kg (N·s/kg), and SI measurements of specific impulse can be written in terms of either units interchangeably. This unit highlights the definition of specific impulse as impulse per unit mass of propellant.

Specific fuel consumption is inversely proportional to specific impulse and has units of g/(kN·s) or lb/(lbf·h). Specific fuel consumption is used extensively for describing the performance of air-breathing jet engines.

Specific impulse in seconds

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Specific impulse, measured in seconds, can be thought of as how many seconds one kilogram of fuel can produce one kilogram of thrust. Or, more precisely, how many seconds a given propellant, when paired with a given engine, can accelerate its own initial mass at 1 g. The longer it can accelerate its own mass, the more delta-V it delivers to the whole system.

In other words, given a particular engine and a mass of a particular propellant, specific impulse measures for how long a time that engine can exert a continuous force (thrust) until fully burning that mass of propellant. A given mass of a more energy-dense propellant can burn for a longer duration than some less energy-dense propellant made to exert the same force while burning in an engine. Different engine designs burning the same propellant may not be equally efficient at directing their propellant's energy into effective thrust.

For all vehicles, specific impulse (impulse per unit weight-on-Earth of propellant) in seconds can be defined by the following equation:

F thrust = g 0 I sp m ˙ , {\displaystyle F_{\text{thrust}}=g_{0}\cdot I_{\text{sp}}\cdot {\dot {m}},}

where:

  • F thrust {\displaystyle F_{\text{thrust}}} is the thrust obtained from the engine (newtons or pounds force),
  • g 0 {\displaystyle g_{0}} is the standard gravity, which is nominally the gravity at Earth's surface (m/s or ft/s),
  • I sp {\displaystyle I_{\text{sp}}} is the specific impulse measured (seconds),
  • m ˙ {\displaystyle {\dot {m}}} is the mass flow rate of the expended propellant (kg/s or slugs/s)

Isp in seconds is the amount of time a rocket engine can generate thrust, given a quantity of propellant whose weight is equal to the engine's thrust.

The advantage of this formulation is that it may be used for rockets, where all the reaction mass is carried on board, as well as airplanes, where most of the reaction mass is taken from the atmosphere. In addition, giving the result as a unit of time makes the result easily comparable between calculations in SI units, imperial units, US customary units or other unit framework.

The specific impulse of various jet engines (SSME is the Space Shuttle Main Engine)

Imperial units conversion

The English unit pound mass is more commonly used than the slug, and when using pounds per second for mass flow rate, it is more convenient to express standard gravity as 1 pound-force per pound-mass. Note that this is equivalent to 32.17405 ft/s2, but expressed in more convenient units. This gives:

F thrust = I sp m ˙ ( 1 l b f l b m ) . {\displaystyle F_{\text{thrust}}=I_{\text{sp}}\cdot {\dot {m}}\cdot \left(1\mathrm {\frac {lbf}{lbm}} \right).}

Rocketry

In rocketry, the only reaction mass is the propellant, so the specific impulse is calculated using an alternative method, giving results with units of seconds. Specific impulse is defined as the thrust integrated over time per unit weight-on-Earth of the propellant:

I sp = v e g 0 , {\displaystyle I_{\text{sp}}={\frac {v_{\text{e}}}{g_{0}}},}

where

  • I sp {\displaystyle I_{\text{sp}}} is the specific impulse measured in seconds,
  • v e {\displaystyle v_{\text{e}}} is the average exhaust speed along the axis of the engine (in m/s or ft/s),
  • g 0 {\displaystyle g_{0}} is the standard gravity (in m/s or ft/s).

In rockets, due to atmospheric effects, the specific impulse varies with altitude, reaching a maximum in a vacuum. This is because the exhaust velocity isn't simply a function of the chamber pressure, but is a function of the difference between the interior and exterior of the combustion chamber. Values are usually given for operation at sea level ("sl") or in a vacuum ("vac").

Specific impulse as effective exhaust velocity

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Because of the geocentric factor of g0 in the equation for specific impulse, many prefer an alternative definition. The specific impulse of a rocket can be defined in terms of thrust per unit mass flow of propellant. This is an equally valid (and in some ways somewhat simpler) way of defining the effectiveness of a rocket propellant. For a rocket, the specific impulse defined in this way is simply the effective exhaust velocity relative to the rocket, ve. "In actual rocket nozzles, the exhaust velocity is not really uniform over the entire exit cross section and such velocity profiles are difficult to measure accurately. A uniform axial velocity, ve, is assumed for all calculations which employ one-dimensional problem descriptions. This effective exhaust velocity represents an average or mass equivalent velocity at which propellant is being ejected from the rocket vehicle." The two definitions of specific impulse are proportional to one another, and related to each other by: v e = g 0 I sp , {\displaystyle v_{\text{e}}=g_{0}\cdot I_{\text{sp}},} where

  • I sp {\displaystyle I_{\text{sp}}} is the specific impulse in seconds,
  • v e {\displaystyle v_{\text{e}}} is the specific impulse measured in m/s, which is the same as the effective exhaust velocity measured in m/s (or ft/s if g is in ft/s),
  • g 0 {\displaystyle g_{0}} is the standard gravity, 9.80665 m/s (in United States customary units 32.174 ft/s).

This equation is also valid for air-breathing jet engines, but is rarely used in practice.

(Note that different symbols are sometimes used; for example, c is also sometimes seen for exhaust velocity. While the symbol I sp {\displaystyle I_{\text{sp}}} might logically be used for specific impulse in units of (N·s)/(m·kg); to avoid confusion, it is desirable to reserve this for specific impulse measured in seconds.)

It is related to the thrust, or forward force on the rocket by the equation: F thrust = v e m ˙ , {\displaystyle F_{\text{thrust}}=v_{\text{e}}\cdot {\dot {m}},} where m ˙ {\displaystyle {\dot {m}}} is the propellant mass flow rate, which is the rate of decrease of the vehicle's mass.

A rocket must carry all its propellant with it, so the mass of the unburned propellant must be accelerated along with the rocket itself. Minimizing the mass of propellant required to achieve a given change in velocity is crucial to building effective rockets. The Tsiolkovsky rocket equation shows that for a rocket with a given empty mass and a given amount of propellant, the total change in velocity it can accomplish is proportional to the effective exhaust velocity.

A spacecraft without propulsion follows an orbit determined by its trajectory and any gravitational field. Deviations from the corresponding velocity pattern (these are called Δv) are achieved by sending exhaust mass in the direction opposite to that of the desired velocity change.

Actual exhaust speed versus effective exhaust speed

When an engine is run within the atmosphere, the exhaust velocity is reduced by atmospheric pressure, in turn reducing specific impulse. This is a reduction in the effective exhaust velocity, versus the actual exhaust velocity achieved in vacuum conditions. In the case of gas-generator cycle rocket engines, more than one exhaust gas stream is present as turbopump exhaust gas exits through a separate nozzle. Calculating the effective exhaust velocity requires averaging the two mass flows as well as accounting for any atmospheric pressure.

For air-breathing jet engines, particularly turbofans, the actual exhaust velocity and the effective exhaust velocity are different by orders of magnitude. This happens for several reasons. First, a good deal of additional momentum is obtained by using air as reaction mass, such that combustion products in the exhaust have more mass than the burned fuel. Next, inert gases in the atmosphere absorb heat from combustion, and through the resulting expansion provide additional thrust. Lastly, for turbofans and other designs there is even more thrust created by pushing against intake air which never sees combustion directly. These all combine to allow a better match between the airspeed and the exhaust speed, which saves energy/propellant and enormously increases the effective exhaust velocity while reducing the actual exhaust velocity. Again, this is because the mass of the air is not counted in the specific impulse calculation, thus attributing all of the thrust momentum to the mass of the fuel component of the exhaust, and omitting the reaction mass, inert gas, and effect of driven fans on overall engine efficiency from consideration.

Essentially, the momentum of engine exhaust includes a lot more than just fuel, but specific impulse calculation ignores everything but the fuel. Even though the effective exhaust velocity for an air-breathing engine seems nonsensical in the context of actual exhaust velocity, this is still useful for comparing absolute fuel efficiency of different engines.

Density specific impulse

A related measure, the density specific impulse, sometimes also referred to as Density Impulse and usually abbreviated as Isd is the product of the average specific gravity of a given propellant mixture and the specific impulse. While less important than the specific impulse, it is an important measure in launch vehicle design, as a low specific impulse implies that bigger tanks will be required to store the propellant, which in turn will have a detrimental effect on the launch vehicle's mass ratio.

Specific fuel consumption

Specific impulse is inversely proportional to specific fuel consumption (SFC) by the relationship Isp = 1/(go·SFC) for SFC in kg/(N·s) and Isp = 3600/SFC for SFC in lb/(lbf·hr).

Examples

For a more comprehensive list, see Spacecraft propulsion § Table of methods.
Rocket engines in vacuum
Model Type First
run
Application TSFC Isp (by weight) Isp (by mass)
lb/lbf·h g/kN·s s m/s
Avio P80 solid fuel 2006 Vega stage 1 13 360 280 2700
Avio Zefiro 23 solid fuel 2006 Vega stage 2 12.52 354.7 287.5 2819
Avio Zefiro 9A solid fuel 2008 Vega stage 3 12.20 345.4 295.2 2895
Merlin 1D liquid fuel 2013 Falcon 9 12 330 310 3000
RD-843 liquid fuel Vega upper stage 11.41 323.2 315.5 3094
Kuznetsov NK-33 liquid fuel 1970s N-1F, Soyuz-2-1v stage 1 10.9 308 331 3250
NPO Energomash RD-171M liquid fuel Zenit-2M, -3SL, -3SLB, -3F stage 1 10.7 303 337 3300
LE-7A cryogenic H-IIA, H-IIB stage 1 8.22 233 438 4300
Snecma HM-7B cryogenic Ariane 2, 3, 4, 5 ECA upper stage 8.097 229.4 444.6 4360
LE-5B-2 cryogenic H-IIA, H-IIB upper stage 8.05 228 447 4380
Aerojet Rocketdyne RS-25 cryogenic 1981 Space Shuttle, SLS stage 1 7.95 225 453 4440
Aerojet Rocketdyne RL-10B-2 cryogenic Delta III, Delta IV, SLS upper stage 7.734 219.1 465.5 4565
NERVA NRX A6 nuclear 1967 869
Jet engines with Reheat, static, sea level
Model Type First
run
Application TSFC Isp (by weight) Isp (by mass)
lb/lbf·h g/kN·s s m/s
Turbo-Union RB.199 turbofan Tornado 2.5 70.8 1440 14120
GE F101-GE-102 turbofan 1970s B-1B 2.46 70 1460 14400
Tumansky R-25-300 turbojet MIG-21bis 2.206 62.5 1632 16000
GE J85-GE-21 turbojet F-5E/F 2.13 60.3 1690 16570
GE F110-GE-132 turbofan F-16E/F 2.09 59.2 1722 16890
Honeywell/ITEC F125 turbofan F-CK-1 2.06 58.4 1748 17140
Snecma M53-P2 turbofan Mirage 2000C/D/N 2.05 58.1 1756 17220
Snecma Atar 09C turbojet Mirage III 2.03 57.5 1770 17400
Snecma Atar 09K-50 turbojet Mirage IV, 50, F1 1.991 56.4 1808 17730
GE J79-GE-15 turbojet F-4E/EJ/F/G, RF-4E 1.965 55.7 1832 17970
Saturn AL-31F turbofan Su-27/P/K 1.96 55.5 1837 18010
GE F110-GE-129 turbofan F-16C/D, F-15EX 1.9 53.8 1895 18580
Soloviev D-30F6 turbofan MiG-31, S-37/Su-47 1.863 52.8 1932 18950
Lyulka AL-21F-3 turbojet Su-17, Su-22 1.86 52.7 1935 18980
Klimov RD-33 turbofan 1974 MiG-29 1.85 52.4 1946 19080
Saturn AL-41F-1S turbofan Su-35S/T-10BM 1.819 51.5 1979 19410
Volvo RM12 turbofan 1978 Gripen A/B/C/D 1.78 50.4 2022 19830
GE F404-GE-402 turbofan F/A-18C/D 1.74 49 2070 20300
Kuznetsov NK-32 turbofan 1980 Tu-144LL, Tu-160 1.7 48 2100 21000
Snecma M88-2 turbofan 1989 Rafale 1.663 47.11 2165 21230
Eurojet EJ200 turbofan 1991 Eurofighter 1.66–1.73 47–49 2080–2170 20400–21300
Dry jet engines, static, sea level
Model Type First
run
Application TSFC Isp (by weight) Isp (by mass)
lb/lbf·h g/kN·s s m/s
GE J85-GE-21 turbojet F-5E/F 1.24 35.1 2900 28500
Snecma Atar 09C turbojet Mirage III 1.01 28.6 3560 35000
Snecma Atar 09K-50 turbojet Mirage IV, 50, F1 0.981 27.8 3670 36000
Snecma Atar 08K-50 turbojet Super Étendard 0.971 27.5 3710 36400
Tumansky R-25-300 turbojet MIG-21bis 0.961 27.2 3750 36700
Lyulka AL-21F-3 turbojet Su-17, Su-22 0.86 24.4 4190 41100
GE J79-GE-15 turbojet F-4E/EJ/F/G, RF-4E 0.85 24.1 4240 41500
Snecma M53-P2 turbofan Mirage 2000C/D/N 0.85 24.1 4240 41500
Volvo RM12 turbofan 1978 Gripen A/B/C/D 0.824 23.3 4370 42800
RR Turbomeca Adour turbofan 1999 Jaguar retrofit 0.81 23 4400 44000
Honeywell/ITEC F124 turbofan 1979 L-159, X-45 0.81 22.9 4440 43600
Honeywell/ITEC F125 turbofan F-CK-1 0.8 22.7 4500 44100
PW J52-P-408 turbojet A-4M/N, TA-4KU, EA-6B 0.79 22.4 4560 44700
Saturn AL-41F-1S turbofan Su-35S/T-10BM 0.79 22.4 4560 44700
Snecma M88-2 turbofan 1989 Rafale 0.782 22.14 4600 45100
Klimov RD-33 turbofan 1974 MiG-29 0.77 21.8 4680 45800
RR Pegasus 11-61 turbofan AV-8B+ 0.76 21.5 4740 46500
Eurojet EJ200 turbofan 1991 Eurofighter 0.74–0.81 21–23 4400–4900 44000–48000
GE F414-GE-400 turbofan 1993 F/A-18E/F 0.724 20.5 4970 48800
Kuznetsov NK-32 turbofan 1980 Tu-144LL, Tu-160 0.72-0.73 20–21 4900–5000 48000–49000
Soloviev D-30F6 turbofan MiG-31, S-37/Su-47 0.716 20.3 5030 49300
Snecma Larzac turbofan 1972 Alpha Jet 0.716 20.3 5030 49300
IHI F3 turbofan 1981 Kawasaki T-4 0.7 19.8 5140 50400
Saturn AL-31F turbofan Su-27 /P/K 0.666-0.78 18.9–22.1 4620–5410 45300–53000
RR Spey RB.168 turbofan AMX 0.66 18.7 5450 53500
GE F110-GE-129 turbofan F-16C/D, F-15 0.64 18 5600 55000
GE F110-GE-132 turbofan F-16E/F 0.64 18 5600 55000
Turbo-Union RB.199 turbofan Tornado ECR 0.637 18.0 5650 55400
PW F119-PW-100 turbofan 1992 F-22 0.61 17.3 5900 57900
Turbo-Union RB.199 turbofan Tornado 0.598 16.9 6020 59000
GE F101-GE-102 turbofan 1970s B-1B 0.562 15.9 6410 62800
PW TF33-P-3 turbofan B-52H, NB-52H 0.52 14.7 6920 67900
RR AE 3007H turbofan RQ-4, MQ-4C 0.39 11.0 9200 91000
GE F118-GE-100 turbofan 1980s B-2 0.375 10.6 9600 94000
GE F118-GE-101 turbofan 1980s U-2S 0.375 10.6 9600 94000
General Electric CF6-50C2 turbofan A300, DC-10-30 0.371 10.5 9700 95000
GE TF34-GE-100 turbofan A-10 0.37 10.5 9700 95000
CFM CFM56-2B1 turbofan C-135, RC-135 0.36 10 10000 98000
Progress D-18T turbofan 1980 An-124, An-225 0.345 9.8 10400 102000
PW F117-PW-100 turbofan C-17 0.34 9.6 10600 104000
PW PW2040 turbofan Boeing 757 0.33 9.3 10900 107000
CFM CFM56-3C1 turbofan 737 Classic 0.33 9.3 11000 110000
GE CF6-80C2 turbofan 744, 767, MD-11, A300/310, C-5M 0.307-0.344 8.7–9.7 10500–11700 103000–115000
EA GP7270 turbofan A380-861 0.299 8.5 12000 118000
GE GE90-85B turbofan 777-200/200ER/300 0.298 8.44 12080 118500
GE GE90-94B turbofan 777-200/200ER/300 0.2974 8.42 12100 118700
RR Trent 970-84 turbofan 2003 A380-841 0.295 8.36 12200 119700
GE GEnx-1B70 turbofan 787-8 0.2845 8.06 12650 124100
RR Trent 1000C turbofan 2006 787-9 0.273 7.7 13200 129000
Jet engines, cruise
Model Type First
run
Application TSFC Isp (by weight) Isp (by mass)
lb/lbf·h g/kN·s s m/s
Ramjet Mach 1 4.5 130 800 7800
J-58 turbojet 1958 SR-71 at Mach 3.2 (Reheat) 1.9 53.8 1895 18580
RR/Snecma Olympus turbojet 1966 Concorde at Mach 2 1.195 33.8 3010 29500
PW JT8D-9 turbofan 737 Original 0.8 22.7 4500 44100
Honeywell ALF502R-5 GTF BAe 146 0.72 20.4 5000 49000
Soloviev D-30KP-2 turbofan Il-76, Il-78 0.715 20.3 5030 49400
Soloviev D-30KU-154 turbofan Tu-154M 0.705 20.0 5110 50100
RR Tay RB.183 turbofan 1984 Fokker 70, Fokker 100 0.69 19.5 5220 51200
GE CF34-3 turbofan 1982 Challenger, CRJ100/200 0.69 19.5 5220 51200
GE CF34-8E turbofan E170/175 0.68 19.3 5290 51900
Honeywell TFE731-60 GTF Falcon 900 0.679 19.2 5300 52000
CFM CFM56-2C1 turbofan DC-8 Super 70 0.671 19.0 5370 52600
GE CF34-8C turbofan CRJ700/900/1000 0.67-0.68 19–19 5300–5400 52000–53000
CFM CFM56-3C1 turbofan 737 Classic 0.667 18.9 5400 52900
CFM CFM56-2A2 turbofan 1974 E-3, E-6 0.66 18.7 5450 53500
RR BR725 turbofan 2008 G650/ER 0.657 18.6 5480 53700
CFM CFM56-2B1 turbofan C-135, RC-135 0.65 18.4 5540 54300
GE CF34-10A turbofan ARJ21 0.65 18.4 5540 54300
CFE CFE738-1-1B turbofan 1990 Falcon 2000 0.645 18.3 5580 54700
RR BR710 turbofan 1995 G. V/G550, Global Express 0.64 18 5600 55000
GE CF34-10E turbofan E190/195 0.64 18 5600 55000
General Electric CF6-50C2 turbofan A300B2/B4/C4/F4, DC-10-30 0.63 17.8 5710 56000
PowerJet SaM146 turbofan Superjet LR 0.629 17.8 5720 56100
CFM CFM56-7B24 turbofan 737 NG 0.627 17.8 5740 56300
RR BR715 turbofan 1997 717 0.62 17.6 5810 56900
GE CF6-80C2-B1F turbofan 747-400 0.605 17.1 5950 58400
CFM CFM56-5A1 turbofan A320 0.596 16.9 6040 59200
Aviadvigatel PS-90A1 turbofan Il-96-400 0.595 16.9 6050 59300
PW PW2040 turbofan 757-200 0.582 16.5 6190 60700
PW PW4098 turbofan 777-300 0.581 16.5 6200 60800
GE CF6-80C2-B2 turbofan 767 0.576 16.3 6250 61300
IAE V2525-D5 turbofan MD-90 0.574 16.3 6270 61500
IAE V2533-A5 turbofan A321-231 0.574 16.3 6270 61500
RR Trent 700 turbofan 1992 A330 0.562 15.9 6410 62800
RR Trent 800 turbofan 1993 777-200/200ER/300 0.560 15.9 6430 63000
Progress D-18T turbofan 1980 An-124, An-225 0.546 15.5 6590 64700
CFM CFM56-5B4 turbofan A320-214 0.545 15.4 6610 64800
CFM CFM56-5C2 turbofan A340-211 0.545 15.4 6610 64800
RR Trent 500 turbofan 1999 A340-500/600 0.542 15.4 6640 65100
CFM LEAP-1B turbofan 2014 737 MAX 0.53-0.56 15–16 6400–6800 63000–67000
Aviadvigatel PD-14 turbofan 2014 MC-21-310 0.526 14.9 6840 67100
RR Trent 900 turbofan 2003 A380 0.522 14.8 6900 67600
GE GE90-85B turbofan 777-200/200ER 0.52 14.7 6920 67900
GE GEnx-1B76 turbofan 2006 787-10 0.512 14.5 7030 69000
PW PW1400G GTF MC-21 0.51 14.4 7100 69000
CFM LEAP-1C turbofan 2013 C919 0.51 14.4 7100 69000
CFM LEAP-1A turbofan 2013 A320neo family 0.51 14.4 7100 69000
RR Trent 7000 turbofan 2015 A330neo 0.506 14.3 7110 69800
RR Trent 1000 turbofan 2006 787 0.506 14.3 7110 69800
RR Trent XWB-97 turbofan 2014 A350-1000 0.478 13.5 7530 73900
PW 1127G GTF 2012 A320neo 0.463 13.1 7780 76300
Specific impulse of various propulsion technologies
Engine Effective exhaust velocity (m/s) Specific impulse (s) Exhaust specific energy (MJ/kg)
Turbofan jet engine (actual V is ~300 m/s) 29,000 3,000 Approx. 0.05
Space Shuttle Solid Rocket Booster 2,500 250 3
Liquid oxygenliquid hydrogen 4,400 450 9.7
NSTAR electrostatic xenon ion thruster 20,000–30,000 1,950–3,100
NEXT electrostatic xenon ion thruster 40,000 1,320–4,170
VASIMR predictions 30,000–120,000 3,000–12,000 1,400
DS4G electrostatic ion thruster 210,000 21,400 22,500
Ideal photonic rocket 299,792,458 30,570,000 89,875,517,874

An example of a specific impulse measured in time is 453 seconds, which is equivalent to an effective exhaust velocity of 4.440 km/s (14,570 ft/s), for the RS-25 engines when operating in a vacuum. An air-breathing jet engine typically has a much larger specific impulse than a rocket; for example a turbofan jet engine may have a specific impulse of 6,000 seconds or more at sea level whereas a rocket would be between 200 and 400 seconds.

An air-breathing engine is thus much more propellant efficient than a rocket engine, because the air serves as reaction mass and oxidizer for combustion which does not have to be carried as propellant, and the actual exhaust speed is much lower, so the kinetic energy the exhaust carries away is lower and thus the jet engine uses far less energy to generate thrust. While the actual exhaust velocity is lower for air-breathing engines, the effective exhaust velocity is very high for jet engines. This is because the effective exhaust velocity calculation assumes that the carried propellant is providing all the reaction mass and all the thrust. Hence effective exhaust velocity is not physically meaningful for air-breathing engines; nevertheless, it is useful for comparison with other types of engines.

The highest specific impulse for a chemical propellant ever test-fired in a rocket engine was 542 seconds (5.32 km/s) with a tripropellant of lithium, fluorine, and hydrogen. However, this combination is impractical. Lithium and fluorine are both extremely corrosive, lithium ignites on contact with air, fluorine ignites on contact with most fuels, and hydrogen, while not hypergolic, is an explosive hazard. Fluorine and the hydrogen fluoride (HF) in the exhaust are very toxic, which damages the environment, makes work around the launch pad difficult, and makes getting a launch license that much more difficult. The rocket exhaust is also ionized, which would interfere with radio communication with the rocket.

Nuclear thermal rocket engines differ from conventional rocket engines in that energy is supplied to the propellants by an external nuclear heat source instead of the heat of combustion. The nuclear rocket typically operates by passing liquid hydrogen gas through an operating nuclear reactor. Testing in the 1960s yielded specific impulses of about 850 seconds (8,340 m/s), about twice that of the Space Shuttle engines.

A variety of other rocket propulsion methods, such as ion thrusters, give much higher specific impulse but with much lower thrust; for example the Hall-effect thruster on the SMART-1 satellite has a specific impulse of 1,640 s (16.1 km/s) but a maximum thrust of only 68 mN (0.015 lbf). The variable specific impulse magnetoplasma rocket (VASIMR) engine currently in development will theoretically yield 20 to 300 km/s (66,000 to 984,000 ft/s), and a maximum thrust of 5.7 N (1.3 lbf).

See also

Notes

References

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  1. 10% better than Trent 700
  2. 10% better than Trent 700
  3. 15 per cent fuel consumption advantage over the original Trent engine
  4. A hypothetical device doing perfect conversion of mass to photons emitted perfectly aligned so as to be antiparallel to the desired thrust vector. This represents the theoretical upper limit for propulsion relying strictly on onboard fuel and the rocket principle.

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